<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we present our results (see our papers), which concern the existence of the renormalized solutions for equations of the type:<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2018-0013_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mo>∂</mo><mi>b</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>-</mo><mtext>div</mtext><mrow><mo>(</mo><mrow><mi>a</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mo>∇</mo><mi>u</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>-</mo><mtext>div</mtext><mrow><mo>(</mo><mrow><mi>Φ</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mi> </mi><mi> </mi><mi> </mi><mtext>in</mtext><mi> </mi><mi>Q</mi><mo>=</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo><mo>,</mo></mrow></math><tex-math>$${{\partial b(x,u)} \over {\partial t}} - {\rm{div}}\left( {a(x,t,u,\nabla u)} \right) - {\rm{div}}\left( {\Phi \left( {x,t,u} \right)} \right) = f\,\,\,{\rm{in}}\,Q = \Omega \times (0,T),$$</tex-math></alternatives></disp-formula>where <italic>b</italic>(<italic>x</italic>, ·) is a strictly increasing <italic>C</italic>1-function for any <italic>x</italic> ∈ Δ, <italic>a</italic>(<italic>x</italic>, <italic>t</italic>, <italic>s</italic>, ξ) and Φ(<italic>x</italic>, <italic>t</italic>, <italic>s</italic>) are a Carathéodory functions. The function <italic>f</italic> is in <italic>L</italic>1(<italic>Q</italic>).</abstract>

In this paper, we present our results (see our papers), which concern the existence of the renormalized solutions for equations of the type:∂b(x,u)∂t-div(a(x,t,u,∇u))-div(Φ(x,t,u))=f   in Q=Ω×(0,T),$${{\partial b(x,u)} \over {\partial t}} - {\rm{div}}\left( {a(x,t,u,\nabla u)} \right) - {\rm{div}}\left( {\Phi \left( {x,t,u} \right)} \right) = f\,\,\,{\rm{in}}\,Q = \Omega \times (0,T),$$where b(x, ·) is a strictly increasing C1-function for any x ∈ Δ, a(x, t, s, ξ) and Φ(x, t, s) are a Carathéodory functions. The function f is in L1(Q).

A few results on some nonlinear parabolic problems in Orlicz-Sobolev spaces

Faculté des Sciences Juridiques, Economiques et Sociales. Université

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"A few results on some nonlinear parabolic problems in Orlicz-Sobolev spaces"}

In this paper, we present our results (see our papers), which concern the existence of the renormalized solutions for equations of the...

A few results on some nonlinear parabolic problems in Orlicz-Sobolev spaces

Published Online: May 16, 2019

Page range: 158 - 170

Received: Feb 25, 2019

Accepted: Apr 15, 2019

DOI: https://doi.org/10.1515/mjpaa-2018-0013

Keywords
Parabolic equation, Orlicz-Sobolev spaces, Renormalized solutions, Unilateral problem

© 2018 Hicham Redwane, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A few results on some nonlinear parabolic problems in Orlicz-Sobolev spaces

Published Online: May 16, 2019

Page range: 158 - 170

Received: Feb 25, 2019

Accepted: Apr 15, 2019

DOI: https://doi.org/10.1515/mjpaa-2018-0013

KeywordsParabolic equation, Orlicz-Sobolev spaces, Renormalized solutions, Unilateral problem

© 2018 Hicham Redwane, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Parabolic equation, Orlicz-Sobolev spaces, Renormalized solutions, Unilateral problem